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This paper aims to increase the manufacturing accuracy and quality of product by improving the prediction accuracy of forecasting compensatory control (FCC).

The dynamic analysis model, which combines grey dynamic model with time series autoregressive integrated moving average (ARIMA) model is proposed. In addition, the Markov chain from stochastic process theory is applied to improve the prediction accuracy.

The proposed model is more accurate than ARIMA model and grey dynamic model.

The paper provides a viewpoint on FCC by using the combined methodology, which takes advantage of high predictable power of grey dynamic model and at the same time takes advantage of the prediction powers of ARIMA model and Markov chain.

The purpose of this paper is to overcome the deficiency of the current GM(1,N) such as low‐prediction precision, extend the scope of GM(1,N) and provide an effective grey dynamic model GM(1,N) for the relationship of cost and variability.

The relationship between two factors of variety and the cost of manufacturing system is studied on the basis of the variety reduction program theory. Based on the Grey system and the gradient algorithm, a Grey dynamic model GM(1,N) is proposed between cost and variety by optimizing the coefficient and background value of the model which is used to check validity for the relation of plasm‐yarn machine product and variety.

The proposed Grey dynamic prediction model GM(1,N) for the relationship of cost and variability has high precision and easy‐to‐use.

A Grey model GM(1,N) for prediction is proposed.

The proposed model should also have potential for multifactor system prediction in engineering.

The deficiency of the current GM(1,N) is overcome, the scope of GM(1,N) is extended and the proposed Grey dynamic model GM(1,N) has high‐prediction precision.

The purpose of this paper is to realize scientific reasoning and prediction in economic catastrophe, which occurs in the short‐term and leads to invalidation of most classical prediction models through lacking basic sample data.

Based on functional theory, grey number algebra theory, Bayesian network theory and interval grey number theory, the authors established GFAM (1,1), which is grey function analysis model (1,1), to excavate and utilize the existing data sufficiently.

This paper proved least squares parameters theorem and prediction theorem and the process of GFAM (1,1). A case was established and demonstrated the utility and good prediction of this model.

This paper established GFAM (1,1), which overcomes the hysteretic defect of classical prediction model and provides a preferable solution in system prediction in economic catastrophe.

Since the issuance in 2009, the digital currency has enjoyed an increasing popularity and has become one of the most important options for global investors. The purpose of this paper is to propose a hybrid model ( KDJ–Markov chain) which integrates the advantages of the stochastic index (KDJ) and grey Markov chain methods and provide a useful decision support tool for investors participating in the digital currency market.

Taking Litecoin's closing price prediction as an example, the closing prices from May 2 to June 20, 2017, are used as the training set, while those from June 21 to August 9, 2017, are used as the test set. In addition, an adaptive KDJ–Markov chain is proposed to enhance the adaptability for dynamic transaction information. And the paper verifies the effectiveness of the KDJ–Markov chain method and adaptive KDJ–Markov chain method.

The results show that the proposed methods can provide a reliable foundation for market analysis and investment decisions. Under the circumstances the accuracy of the training set and the accuracy of the test set are 76% and 78%, respectively.

This study not only solves the problems that KDJ method cannot accurately predict the next day's state and the grey Markov chain method cannot divide the states very well, but it also provides two useful decision support tools for investors to make more scientific and reasonable decisions for digital currency where there are no existing methods to analyze the fluctuation.

A new approach to analyze the fluctuation of digital currency, in which there are no existing methods, is proposed based on the stochastic index (KDJ) and grey Markov chain methods. And both of these two models have high accuracy.

The purpose of this paper is to overcome the weakness of the traditional model, in which the grey action quantity is a real number and thus leads to a “unique solution” and to build the model with a trapezoidal possibility degree function.

Using the system input and output block diagram of the model, the interval grey action quantity is restored under the condition of insufficient system influencing factors, and the trapezoidal possibility degree function is formed. Based on that, a new model able to output non-unique solutions is constructed.

The model satisfies the non-unique solution principle of the grey theory under the condition of insufficient information. The model is compatible with the traditional model in structure and modelling results. The validity and practicability of the new model are verified by applying it in simulating the ecological environment water consumption in the Yangtze River basin.

In this study, the interval grey number form of grey action quantity is restored under the condition of insufficient system influencing factors, and the unique solution to the problem of the traditional model is solved. It is of great value in enriching the theoretical system of grey prediction models.

Taking power consumption as an example, the accurate prediction of the future power consumption level is related to the utilization efficiency of the power infrastructure investment. If the prediction of the power consumption level is too low, it will lead to the insufficient construction of the power infrastructure and the frequent occurrence of “power shortage” in the power industry. If the prediction is too high, it will lead to excessive investment in the power infrastructure. As a result, the overall surplus of power supply will lead to relatively low operation efficiency. Therefore, building an appropriate model for the correct interval prediction is a better way to solve such problems. The model proposed in this study is an effective one to solve such problems.

A new grey prediction model with its interval grey action quantity based on the trapezoidal possibility degree function is proposed for the first time.

The purpose of this paper is to develop a small data set forecasting method to improve the effectiveness when making managerial decisions.

In the grey modeling process, appropriate background values are one of the key factors in determining forecasting accuracy. In this paper, grey compensation terms are developed to make more appropriate background values to further improve the forecasting accuracy of grey models.

In the experiment, three real cases were used to validate the effectiveness of the proposed method. The experimental results show that the proposed method can improve the accuracy of grey predictions. The results further indicate that background values determined by the proposed compensation terms can improve the accuracy of grey model in the three cases.

Previous studies determine appropriate background values within the limitation of traditional grey modeling process, while this study makes new background values without the limitation. The experimental results would encourage researchers to develop more accuracy grey models without the limitation when determining background values.

The purpose of this paper is to develop a novel multivariate fractional grey model termed GM(a, n) based on the classical GM(1, n) model. The new model can provide accurate prediction with more freedom, and enrich the content of grey theory.

The GM(α, n) model is systematically studied by using the grey modelling technique and the forward difference method. The optimal fractional order a is computed by the genetic algorithm. Meanwhile, a stochastic testing scheme is presented to verify the accuracy of the new GM(a, n) model.

The recursive expressions of the time response function and the restored values of the presented model are deduced. The GM(1, n), GM(a, 1) and GM(1, 1) models are special cases of the model. Computational results illustrate that the GM(a, n) model provides accurate prediction.

The GM(a, n) model is used to predict China’s total energy consumption with the raw data from 2006 to 2016. The superiority of the GM(a, n) model is more freedom and better modelling by fractional derivative, which implies its high potential to be used in energy field.

It is the first time to investigate the multivariate fractional grey GM(α, n) model, apply it to study the effects of China’s economic growth and urbanization on energy consumption.

The purpose of this paper is to forecast the future trend of Ghana’s total energy consumption (GTEC) using two grey models, which are GM(1,1) and the grey Verhulst model.

The paper employs the use of Even model GM(1,1) and the grey Verhulst model to forecast GTEC for the next five years. Since various models were used, the margin for error is minimal, hence resulting in a better choice for forecasting the future. The forecast reveals that the GTEC for the next five years will increase rapidly.

The results reveal that the models can be used accurately to predict the total energy consumption smoothly. This will aid the government of Ghana to take necessary measures such as transforming the economic development pattern and enhancing the energy utilization efficiency since future patterns of energy consumed can be predicted.

This research is meaningful to the government and all stakeholders in Ghana to help develop and appreciate the energy sector and its economic impact. This research is going to help government put in measures for efficient utilization of energy since results reveal an increase in energy consumption.

Research results could be used for development of the energy sector through managerial and economic decision making.

Ghana is a developing country and has great prospects in terms of boosting or resourcing its energy sector to meet future demands. The successfully explored models could aid the government of Ghana to formulate policies in the energy sector and generate future consumption plans.

The purpose of this paper is to study a fractional grey model FAGM(1,1,t^α) based on the GM(1,1,t^α) model and the fractional accumulated generating operation, and then predict the national health expenditure, the government health expenditure and the out-of-pocket health expenditure of China.

The presented univariate grey model is systematically studied by using the grey modelling technique, the fractional accumulated generating operation and the trapezoid approximation formula of definite integral. The optimal system parameters r and α are evaluated by the particle swarm optimisation algorithm.

The expressions of the time response function and the restored values of this model are derived. The GM(1,1), NGM(1,1,k,c) and GM(1,1,t^α) models are particular cases of the FAGM(1,1,t^α) model with deterministic r and α. Compared with other forecasting models, the results of the FAGM(1,1,t^α) model have higher precision.

The superiority of the new model has high potential to be used in the medicine and health fields and others. Results can provide a guideline for government decision making.

The univariate fractional grey model FAGM (1,1,t^α) successfully studies the China’s health expenditure.

Given the effects of natural and social factors, data on both the supply and demand sides of electricity will produce obvious seasonal fluctuations. The purpose of this article is to propose a new dynamic seasonal grey model based on PSO-SVR to forecast the production and consumption of electric energy.

In the model design, firstly, the parameters of the SVR are initially optimized by the PSO algorithm for the estimation of the dynamic seasonal operator. Then, the seasonal fluctuations in the electricity demand data are eliminated using the dynamic seasonal operator. After that, the time series after eliminating of the seasonal fluctuations are used as the training set of the DSGM(1, 1) model, and the corresponding fitted, and predicted values are calculated. Finally, the seasonal reduction is performed to obtain the final prediction results.

This study found that the electricity supply and demand data have obvious seasonal and nonlinear characteristics. The dynamic seasonal grey model based on PSO-SVR performs significantly better than the comparative model for hourly and monthly data as well as for different time durations, indicating that the model is more accurate and robust in seasonal electricity forecasting.

Considering the seasonal and nonlinear fluctuation characteristics of electricity data. In this paper, a dynamic seasonal grey model based on PSO-SVR is established to predict the consumption and production of electric energy.